To be honest I don't think any type of paint applied to a bird cage after the fact is a good idea.
The paint that is applied to a bird cage is the negatively charged powder type that is typical in industrial processes where you want to ensure a strong long term bond to a smooth metal surface. The metal cage pieces are positively charged while the paint is negatively charged causing the paint to adhere better than any DIY'er could do.
If you attempt to paint the cage after the fact then likely it will chip off easily during cleaning, during beak sharpening or simply because rust will start forming underneath the paint and causing it to bubble. Instead of painting I would suggest using a scour pad to rub off invasive rust as it forms, especially along the bottom of the cage where it is exposed to corrosive bird droppings. As long as you keep up with this on a bi-weekly basis then you can get decades more life out of a rusty old cage.